Lomborg writes (p. 64) that 1941 is still the varmest year recorded on Greenland, and that the 1930s and 1940s still are the two warmest decades there.
    In response to this, John Cappelen, meteorologist at the Danish Meteorological Institutet, DMI, says that the truth is more complicated, because Greenland is large, and the trends are not the same at the seven stations where temperatures have been followed. He also says that at the east coast, 2003 is the warmest year on record, whereas at Nuuk (the "capital", situated in south west Greenland), 1941 and 2003 were equally warm. Altogether, the record year is 2003 rather than 1941.
     The temperatures for three weather stations at the west coast of Greenland are to be found on the internet here. The average for Nuuk was +0.83° in 1941, and +0.51° in 2003, i.e. slightly lower. So Lomborg is right as to the west coast of Greenland, but not as to Greenland in total.
   It may be added that the extent of ice melting on Greenland is steadily increasing, see here and here. The most recent information is that the extent of melting reached a new record in 2007, and that air temperatures above the ice are have increased by about  4° C since 1991, see this link.
    Remember that melting consumes heat energy and tends to lower temperatures. If you put a clump of ice in a jar and supply a heat source to melt the ice slowly, the temperature in the jar will remain constant - at exactly 0° C - as long as there is still ice left in the jar. It is only when all ice has melted that water temperatures start to rise. So if there is a lack of local temperature rise at the weather stations at the coast, this cannot be used as an argument that there is no increase in ice melting.
   The temperature trends for Greenland are not typical for the whole arctic region, as is evident in Przybylak (2000), cited by Lomborg.

Lomborg writes (p. 65) that the only part of Antarctica that is warming is the west Antarctic peninsula which makes out only 4  % of the total land area; the remaining 96 % has become colder. But this is not true.
    Temperatures for those Antarctic weather stations with the longest time series are found at this link. It is seen here that since the mid 20th century, annual temperatures have increased significantly at the west Antarctic Peninsula and in one coastal station on mainland Antarctica. At all other weather stations, including the South Pole, there is no significant trend. In a few stations there is a significant negative trend for autumn temperatures, but not for annual temperaturs.
    Others have said the same as Lomborg, viz. that 96 % of the Antarctic continent is cooling. This information goes back to a paper by Peter Doran et al. in 2002 in Nature (link). They found (by a different type of analysis) that 58 % of Antarctica had cooled from 1966 to 2000, especially regarding autumn temperatures, whereas the rest, i.e. 42 %, had warmed, including the west Antarctic peninsula that makes out 15 % of the area.
   The cooling of parts of the continent is partially due to the ozone hole. According to Doran, as the ozone hole heals - thanks to worldwide bans on ozone-destroying chemicals - all of Antarctica is likely to warm with the rest of the planet.
    The summary of the paper in Nature pointed out how the cooling trend posed challenges to models of Antarctic climate. American newspaper and television reports focused on this part of the paper, and claimed that these scientific findings ran counter to the theory of global warming. Since then, climate skeptics have cited this information over and over again. Although the scientists have written rebuttals and explained that the media have misunderstood the information, the misinsterpretation has quickly become legend among skeptics, and is cited ever more often. A refutation written by Peter Doran in The New York Times may be read here.
  

Lomborg criticises the way that the decline of a population of emperor penguins is presented in Al Gore´s  book "An Inconvenient  Truth". However, as explained on the Lomborg-errors page on Al Gore, for page 178 in Gore´s book, there is very little flaw in Al Gore´s text. On the basis of data from G.L. Kooyman, Lomborg infers that there may have been increases in certain emperor penguin populations on the Ross ice shelf; however, a new paper co-authored by Kooyman states that the colonies referred to have had no significant changes up to now, except that one out of six colonies (one not referred to by Lomborg) has had a small increase. Also, new information from 2009 says that the studied colony of emperor penguins is expected to decline very much during this century because fo changes in sea ice (Jenouvrier & Caswell (2009): Proceedings national academy of sciences USA 106(6): 1844-1847).
As to Adélie penguins, which require winter pack ice, Lomborg only talks about increase, referring to a site in east Antarctica. But, according to WWF, the species is severely declining in some places and increasing in others (link). One of the references that Lomborg has read (Vaughan 2001) talks about a colony that has persisted by at least 600 years, but which is now declining. Lomborg omits to mention that.

Flaws on particular pages in Lomborgs text:

FLAW
Page 63 top (various end notes)
Flaw: The references to the IPCC report that are written as fig. 10.6.1, fig. 10.6.3 and fig. 10.6.4 should actually have been paragraph 10.6.1, paragraph 10.6.3 and paragraph 10.6.4.

FLAW
Page 63 top: "Antarctica will not noticeably start melting . . . actually be accumulating ice . . .  "
Flaw: This is not true, and it relies on Lomborg´s selective reading of his sources. See the review articles at the top of this page for better and more recent information.

FLAW
Page 63 bottom: "Some analyses have shown more rapid loss in recent years  . . .  "
Flaw: This is a biased wording. All analyses have shown much more rapid loss in recent years. Lomborg´s statement that by early 2007 two of the major glaciers in Greenland were again seen reverting to much lower rates is not justified. He cannot, when writing his book in 2007, base anything on what has happened just within that same year. A person with alleged expertise in statistics should never extrapolate a trend from just one year and suggest that this might tell anything about what we could expect in the future. Actually, the rapid loss has continued after 2007, and the data strongly suggest an ever accelerating mass loss, as described in the papers listed at the top of this page (Cazenave; Allison). Lomborg´s note has an estimate of a contribution from Greenland to sea level rise of about 0.28 mm per year. Since then, this estimate has nearly tripled to  0.75 mm per year after 2006 (van den Broeke et al. (2009): Science 326: 984-986.)

FLAW
Page 63 bottom: "Even with the most extreme estimates of Greenland melting  . . .  "
Flaw: This does not fully agree with the paper by Parizek & Alley that Lomborg has read. Here, on page 1023, their worst case scenario has a contribution from Greenland to sea level rise of 5.82 m by the year 2500.

FLAW
Page 63 bottom - page 64 top: "In a recent overview of all the major models  . . .  "
Flaw: Lomborg refers to a paper by Oerlemans et al. (2005). It reports runs with five climate models, few are none of which are AOGCMs (i.e. they do not include both atmosphere and ocean). They are all performed on IPCC´s B2 scenario, in which the emission of CO2 grows considerably more slowly than what is actually the case at present. Furthermore "the dynamic response of glaciers is not considered", i.e. the types of acceleration of glaciers that is seen recently are disregarded. Therefore, the model outputs have less melting than what may actually be expected. Lomborg´s term "all the major models" suggests to the reader that all likely outcomes are covered by the study, which is not the case, as it deals only with the B2 scenario.

FLAW
Page 64 top: "In another overview, all models clearly show  . . .  "
Flaw: Lomborg relies much on the reference Gregory & Huybrechts (2006). However, this paper suffers from a shortcoming which was also seen in Oerlemans et al. (2005):  it does not include dynamical responses of glaciers. It says in the first paragraph: "Such accelerated flow leads to increased ice discharge into the ocean, but the relevant dynamical processes are not properly understood nor included . . . This therefore represents an important uncertainty for predictions of sea level, but one which is beyond the scope of this paper to address." So the Gregory & Huybrechts paper does not deal with all contributions to sea level rise. Actually, the present state of knowledge (2010), as stated in the papers cited on top of this page, is that Greenland as well as Antarctica give a net contribution to sea level rise.

FLAW
Page 64: "The IPCC estimates that the very worst additional increase . . .  "
Flaw: Here Lomborg refers to a paper by Parizek & Alley that estimates the possible extra melt of Greenland ice that may occur if dynamic response of glaciers turns out to be important. The estimate is that this may contribute with up to 20 cm of extra sea level rise in this century. There are three scenarios, with temperature increases over Greenland by 2130 of 3.2°, 5.8° and 8.4° C, respectively. The scenario with the highest temperature rise corresponds roughly to the most C-intensive IPCC scenario (A1FI). The actual rate of increase in CO2 concentrations by now is actually a little higher than this worst IPCC scenario (links here and here), that is, if present trends continue, the situation will correspond to more than an 8.4° C temperature increase over Greenland, which will yield the 20 cm extra sea level rise referred to above. However, the paper states (p. 1020) that the climate computer model used falls toward the low end of sensitivities. So in reality the rise could possibly be even larger.

ERROR
Page 65: ". . while the other 96 percent of Antarctica has cooled "
Error: This is not true. Lomborg gives three references. The first is Chapman & Walsh (2005), which has now been published in Journal of Climate 20 (16): 4096-4117. According to this paper, there has been a generally warming trend for the Antarctic continent for the period 1958-2002. In most parts of the continent, this trend is not significant. Only small parts of the continent have seen a cooling trend. The second is a website of a climate-sceptic (Humlum). The third is an unpublished talk; the authors of that talk have later (2007) published a paper in which new Antarctic temperature analysis suggests recent warming. As explained above, the claim that 96 percent has cooled is a mistake derived from the media´s false interpretation of a paper by Doran et al. (2002). It is peculiarly troubling that Lomborg´s claim is against the contents of two of his sources.

FLAW
Page 65: "The South Pole has seen its temperature decline . . . "
Flaw: As stated above, there is no significant temperature decline at the South Pole, maybe not even a decline at all (Chapman & Walsh 2005, cited above).

ERROR
Page 65: ". . believing that Larsen B has been intact . . .  "
Error: Larsen B has indeed been intact continuously since the last ice age. It is true that parts of "the Larsen area" had its ice sheets broken up some thousand years ago, but these parts were further to the north, including the Larsen A ice shelf (Pudsey et al. 2006, cited by Lomborg). Larsen B has not been broken up (E. Domack et al. (2005): Nature 436 (3908): 681-685), and its breakup in 2002 when summer temperatures were unusually warm is therefore an indication of more warmth than ever before since the last ice age. Lomborg has seen a paper by Marshall et al. (2006), which refers to the Domack paper and says: "Marine sediments from below where the farthest
south of these sections, the Larsen B shelf, was formerly located, indicate that its collapse is unique within the Holocene period." So Lomborg knew this, but stated otherwise in this text.

<FLAW
Page 65 bottom - 66 top: "While it probably led to ice shelves floating more quickly . . . "
Flaw: This is an understatement. After the collapse of the Larsen B ice shelf, the movement of inland glaciers behind the ice shelf accelerated by a factor of 2 to 8 (Rignot et al (2004): Geophys res. lett. 31(18): L18401; Scambos et al. (2004): Geophys res. lett. 31(18): L18401; Rignot (2006): Phil- trans. Royal Soc. A 364: 1637-1655.)

ERROR
Page 66 top: "The precipitation on the Antarctic Peninsula is increasing . . . and this likely outweighs the melting "
Error: Lomborg´s use of the references is very selective here. For instance he cites Zwally et al. (2005) in which there is a single station on the peninsula showing net accumulation of ice, whereas the same study shows that West Antarctica in total has a large net loss of ice. Morris and Mulvaney (2004) indicate a net increase of ice on the peninsula with future warming (which gives more precipitation), and state that for each degree of warming, the effect on global sea level will be ÷ 0.006 mm. However, warming will also increase the discharge of glacier ice by ablation, that is melting, sublimation and calving, and for each degree of temperature rise, this will contribute + 0.07 mm to global sea level, provided that meltwater can find its way into the sea. Thus, the net effect of melting may be much greater than the net effect of snow accumulation. Although Lomborg touches on this aspectin his note, he avoids the crucial circumstance that precipitation will probably not outweigh melting. This is deliberate distortion of the information he has read. 

FLAW:
Page 66 top: " . . . the Antarctic Peninsula is probably participating in an overall lowering of sea levels."
Flaw: There are indications to the opposite. Firstly, Morris & Mulvaney (2004) indicate that the removal of ice by various processes, especially melting,  may possibly outweigh snow accumulation in the future. This was explained above. In addition, however, there is an effect of accelerating glaciers. Because glaciers are thinning at their ends, they are now moving faster towards the sea than before. This is described in Pritchard & Vaughan (2007): Journal of geophysical research 112 F03S29. They estimate that the net contribution of the Antarctic Peninsula to global sea level from this glacier acceleration and other processes is + 0.16 mm per year. Also van de Berg et al. (2006): Journal of geophysical research 111 D1104 find that the mass balance of the peninsula is probably negative. This is directly opposite what Lomborg states.

ERROR
Page 66: "This too is the story of the continent."
Error: No, it is not. For instance, Lomborg has cited Zwally et al. (2005) as a source for accumulation of ice and snow on the peninsula. But in the same source there is a total estimate of mass gain or loss on Antarctica. There is an estimated total loss of 47 gigaton ice on the whole of west Antarctica, which is not fully conuterbalanced by an estimated gain of 16 giga ton on east Antarctica. This gives a net loss of 31 giga tons per year, which contributes to sea level increase, not decrease. When Lomborg has read this, but nevertheless says the opposite, he is deliberately misleading. Many other references likewise indicate a net loss of ice on the Antarctic continent.

ERROR
Page 66 - 67 top: " . . . a decrease in sea levels in all models. "
Error: This is contrary to the contents of the 2007 IPCC report WG 1, according to which Antarctica gives a net positive contribution to sea level rise. Lomborg does not indicate which models he is talking about. But in the British version of the book, he refers to the paper by Gregory & Hubrechts, which has the shortcomings described above for page 64 top. 

ERROR
Page 67 top: " . . . all models predict ever more net accumulation over this century. "
Error: This is contrary to the trends right now, when there is probably an increasing net contribution to sea level rise (see for instance Allison et al. 2009, cited at the start of this page).  See also the previous comment here.